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A note on "the censored newsvendor and the optimal acquisition of information".

Article Excerpt
This paper revisits the finite-horizon model of a censored newsvendor by Ding et al. [Ding, X., M. L. Puterman, A. Bisi. 2002. The censored newsvendor and the optimal acquisition of information. Oper. Res. 50 517-527]. An important result claimed there without a proper proof is that the myopic order quantity is always less than or equal to the optimal order quantity. Lu et al. [Lu, X., J. S. Song, K. Zhu. 2008. Analysis of perishable inventory systems with censored demand data. Oper. Res. 56(4) 1034-1038.] supplied a correct proof of the result. We analyze the same model using the interesting concept of the unnormalized probability, which simplifies the dynamic programming equation considerably and facilitates the proof of the claim. Moreover, it produces the proof of the existence of an optimal solution for an infinite-horizon setting of the problem.

Subject classifications: inventory/production: unknown demand; censoring; optimal policies.

Area of review: Stochastic Models.

History: Received January 2007; revisions received June 2007, November 2007; accepted February 2008. Published online in Articles in Advance February 9, 2009.

1. Preliminaries

We consider the censored newsvendor problem of Ding, Puterman, and Bisi (2002), referred to as DPB. In DPB, the demand that depends on an unknown parameter is fully observed in a period when it is satisfied from the available inventory. Otherwise, only the event that the demand is larger than or equal to the inventory is observed. This is a problem with partial observations (e.g., Bensoussan et al. 2005). It is formulated as a dynamic program (DP) whose state is the conditional distribution of the parameter given the censored demand observations.

DPB claims that the myopic order quantity is always smaller than or equal to the optimal order quantity. This claim also appears in Chen and Plambeck (2008) and Bisi and Dada (2007), who study, respectively, product substitution with discrete demands and optimal pricing. Although the claim is true, its proof in DPB, in the case of more than two periods in the planning horizon, is found to be erroneous independently by Lu et al. (2005) and the first author...

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